Friction in Gravitational Waves: a test for early-time modified gravity

Modified gravity theories predict in general a non standard equation for the propagation of gravitational waves. Here we discuss the impact of modified friction and speed of tensor modes on cosmic microwave polarization B modes. We show that the non standard friction term, parametrized by $\alpha_{M}$, is degenerate with the tensor-to-scalar ratio $r$, so that small values of $r$ can be compensated by negative constant values of $\alpha_M$. We quantify this degeneracy and its dependence on the epoch at which $\alpha_{M}$ is different from the standard, zero, value and on the speed of gravitational waves $c_{T}$. In the particular case of scalar-tensor theories, $\alpha_{M}$ is constant and strongly constrained by background and scalar perturbations, $0\le \alpha_{M}< 0.01$ and the degeneracy with $r$ is removed. In more general cases however such tight bounds are weakened and the B modes can provide useful constraints on early-time modified gravity.